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cos(tansqrt(x+1))...

`cos(tansqrt(x+1))`

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The correct Answer is:
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Let ` y=cos(tansqrt(x+1))`
`:. (dy)/(dx) = d/(dx)cos(tansqrt(x+1))=-sin(tansqrt(x+1)).(d)/(dx)(tansqrt(x+1))`.
`= -sin(tansqrt(x+1)). sec^(2)sqrt(x+1).(d)/(dx)(x+1)^(1//2) , [:' (d)/(dx) (tanx) = sec^(2)x]`
`= - sin(tansqrt(x+1)). (secsqrt(x+1))^(2).(1)/(2)(x+1)^(-1//2).(d)/(dx)(x+1)`
`= (-1)/(2sqrt(x+1)).sin(tansqrt(x+1)).sec^(2)(sqrt(x+1))`
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